On Thu, 20 May 2004, Gaunce Lewis wrote:
I have encountered a situation in which I have two categories C, D which are related by a pair of adjoint functors L from C to D and R from D to C. Also, there is a cotriple S on C and a cotriple T on D. Finally, there is a natural isomorphism f from RT to SR. It seems that if a couple of diagrams relating f to the structure maps of the cotriples commute, then there is an induced adjoint pair relating the two coalgebra categories. Is this, or something similar to it, in the literature in some easily referenced place?
Thanks, Gaunce
See (for the dual situation) an old paper of mine: Adjoint lifting theorems for categories of algebras, Bull London Math. Soc. 7 (1975), 294--297. I should say (before others say it for me) that this was not the first place the result appeared: it (and much more) was in the famous unpublished (and largely unwritten) thesis of Bill Butler. But Gaunce asked for a published reference. Peter Johnstone